Increasing attention is being paid to the study of families of subsets of an n-set that contain
no subposet P. Especially, we are interested in such families of maximum size given P and …

Three $ k $-dimensional subspaces $ A $, $ B $, and $ C $ of an $ n $-dimensional vector
space $ V $ over a finite field are called a $3 $-cluster if $ A\cap B\cap C=\{\mathbf {0} _V\} …

A zero-sum flow of a graph G is an element of the nullspace of the incidence matrix of G
whose entries are nonzero real numbers. A zero-sum flow is called a k-flow if all the entries …

Let n be a positive integer, qa power of a prime, and ℒ n (q) L_n(q) the poset of subspaces
of an n-dimensional vector space over a field with q elements. This poset is a normalized …

We prove a general lemma (inspired by a lemma of Holroyd and Talbot) about the
connection of the largest cardinalities (or weight) of structures satisfying some hereditary …

For two posets $ P $ and $ Q $, we say $ Q $ is $ P $-free if there does not exist any order-
preserving injection from $ P $ to $ Q $. The speical case for $ Q $ being the Boolean lattice …

Given a finite poset P, the intensively studied quantity L a (n, P) denotes the largest size of a
family of subsets of n not containing P as a weak subposet. Burcsi and Nagy (J. Graph …

The overarching theme of the thesis is the investigation of extremal problems involving
forbidden partially ordered sets (posets). In particular, we will be concerned with the function …

Increasing attention is being paid to the study of families of subsets of an nset that contain no
subposet P. Especially, we are interested in such families of maximum size given P and n …